An Australian Mathematical Winter School run by ARC Laureate Professor Andrew Hassell at the Mathematical Sciences Institute, Australian National University. This is a two-week intensive winter school, taught by Andrew Hassell with two other distinguished researchers from Australia and the USA. The goal of the course is to show how, through microlocal propagation estimates, one can find Fredholm realisations of non-elliptic operators typically encountered in partial differential equations, such as wave operators, Klein-Gordon operators, or Helmholtz operators.